Influence of particle size on the vibration of plates loaded with granular material

Acoustic methods of land mine detection rely on the vibrations of the top plate of the mine in response to sound. For granular soil (e.g., sand), it is expected that particle size will influence the mine response. This hypothesis is studied experimentally using a plate loaded with dry sand of various sizes from hundreds of microns to a few millimeters. For low values of sand mass, the plate resonance decreases and eventually reaches a minimum without particle size dependence. After the minimum, the frequency increase with additional mass includes a particle-size effect. Analytical continuum models for granular media applied to this problem do not accurately capture the particle-size effect. In addition, a continuum-based finite element model (FEM) of a two-layer plate is used with the sand layer replaced by an equivalent elastic layer. For a given thickness of the sand layer and corresponding experimental resonance, an inverse FEM problem is solved iteratively. The effective Young's modulus and bending stiffness of the equivalent elastic layer that match the experimental frequency are found for every layer thickness. Smaller particle sizes are shown to be more compliant in bending. The results clarify the importance of particle size on acoustic detection methods.